LMFDB - Embedded newform 936.2.w.j.307.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(307,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.307"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.10
Character	$\chi$	$=$	936.307
Dual form			936.2.w.j.811.10

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34492 - 0.437240i) q^{2} +(1.61764 - 1.17611i) q^{4} +(-1.98058 + 1.98058i) q^{5} +(-3.05943 - 3.05943i) q^{7} +(1.66136 - 2.28908i) q^{8} +(-1.79774 + 3.52971i) q^{10} +(1.08518 - 1.08518i) q^{11} +(-3.57990 + 0.429300i) q^{13} +(-5.45240 - 2.77699i) q^{14} +(1.23353 - 3.80505i) q^{16} -5.70052i q^{17} +(-4.39498 - 4.39498i) q^{19} +(-0.874489 + 5.53324i) q^{20} +(0.984999 - 1.93397i) q^{22} +2.95135 q^{23} -2.84537i q^{25} +(-4.62699 + 2.14265i) q^{26} +(-8.54727 - 1.35084i) q^{28} +6.96062i q^{29} +(3.05943 - 3.05943i) q^{31} +(-0.00471188 - 5.65685i) q^{32} +(-2.49250 - 7.66677i) q^{34} +12.1189 q^{35} +(-5.14026 - 5.14026i) q^{37} +(-7.83257 - 3.98925i) q^{38} +(1.24323 + 7.82415i) q^{40} +(2.77963 + 2.77963i) q^{41} -3.00392i q^{43} +(0.479142 - 3.03172i) q^{44} +(3.96934 - 1.29045i) q^{46} +(-6.40146 - 6.40146i) q^{47} +11.7202i q^{49} +(-1.24411 - 3.82681i) q^{50} +(-5.28610 + 4.90481i) q^{52} +4.28172i q^{53} +4.29856i q^{55} +(-12.0861 + 1.92044i) q^{56} +(3.04346 + 9.36150i) q^{58} +(-3.00033 + 3.00033i) q^{59} +1.13106i q^{61} +(2.77699 - 5.45240i) q^{62} +(-2.47974 - 7.60598i) q^{64} +(6.24001 - 7.94053i) q^{65} +(7.39889 + 7.39889i) q^{67} +(-6.70444 - 9.22140i) q^{68} +(16.2989 - 5.29885i) q^{70} +(3.20281 - 3.20281i) q^{71} +(7.87480 - 7.87480i) q^{73} +(-9.16078 - 4.66573i) q^{74} +(-12.2785 - 1.94053i) q^{76} -6.64004 q^{77} +4.46803i q^{79} +(5.09309 + 9.97930i) q^{80} +(4.95376 + 2.52303i) q^{82} +(9.78962 + 9.78962i) q^{83} +(11.2903 + 11.2903i) q^{85} +(-1.31343 - 4.04004i) q^{86} +(-0.681180 - 4.28693i) q^{88} +(-4.24001 + 4.24001i) q^{89} +(12.2659 + 9.63903i) q^{91} +(4.77422 - 3.47111i) q^{92} +(-11.4085 - 5.81050i) q^{94} +17.4092 q^{95} +(-11.5753 - 11.5753i) q^{97} +(5.12453 + 15.7627i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{8} - 8 q^{11} - 36 q^{14} + 28 q^{16} + 20 q^{19} + 20 q^{20} + 20 q^{22} - 12 q^{26} - 16 q^{28} + 30 q^{32} + 16 q^{34} - 16 q^{35} + 36 q^{40} + 12 q^{41} + 32 q^{44} - 44 q^{46} + 36 q^{50}+ \cdots - 68 q^{98}+O(q^{100}) $ 24 * q + 6 * q^8 - 8 * q^11 - 36 * q^14 + 28 * q^16 + 20 * q^19 + 20 * q^20 + 20 * q^22 - 12 * q^26 - 16 * q^28 + 30 * q^32 + 16 * q^34 - 16 * q^35 + 36 * q^40 + 12 * q^41 + 32 * q^44 - 44 * q^46 + 36 * q^50 + 4 * q^52 + 32 * q^58 + 16 * q^59 + 76 * q^65 + 28 * q^67 - 32 * q^68 - 40 * q^70 - 8 * q^73 + 32 * q^74 - 36 * q^76 + 32 * q^80 + 72 * q^83 - 4 * q^86 - 28 * q^89 - 4 * q^91 - 32 * q^92 + 28 * q^94 + 24 * q^97 - 68 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.34492	−	0.437240i	0.951005	−	0.309175i
$2$	1.34492	−	0.437240i	0.951005	−	0.309175i
$3$		0			0
$3$		0			0
$4$	1.61764	−	1.17611i	0.808821	−	0.588055i
$5$	−1.98058	+	1.98058i	−0.885741	+	0.885741i	−0.994111	−	0.108370i	$-0.965437\pi$
$5$	−1.98058	+	1.98058i	−0.885741	+	0.885741i	0.108370	+	0.994111i	$0.465437\pi$
$6$		0			0
$7$	−3.05943	−	3.05943i	−1.15635	−	1.15635i	−0.985254	−	0.171100i	$-0.945268\pi$
$7$	−3.05943	−	3.05943i	−1.15635	−	1.15635i	−0.171100	−	0.985254i	$-0.554732\pi$
$8$	1.66136	−	2.28908i	0.587381	−	0.809311i
$9$		0			0
$10$	−1.79774	+	3.52971i	−0.568495	+	1.11619i
$11$	1.08518	−	1.08518i	0.327194	−	0.327194i	−0.524325	−	0.851518i	$-0.675682\pi$
$11$	1.08518	−	1.08518i	0.327194	−	0.327194i	0.851518	+	0.524325i	$0.175682\pi$
$12$		0			0
$13$	−3.57990	+	0.429300i	−0.992886	+	0.119066i
$13$	−3.57990	+	0.429300i	−0.992886	+	0.119066i
$14$	−5.45240	−	2.77699i	−1.45721	−	0.742182i
$15$		0			0
$16$	1.23353	−	3.80505i	0.308383	−	0.951262i
$17$		−	5.70052i		−	1.38258i	−0.722578	−	0.691290i	$-0.757043\pi$
$17$		−	5.70052i		−	1.38258i	0.722578	−	0.691290i	$-0.242957\pi$
$18$		0			0
$19$	−4.39498	−	4.39498i	−1.00828	−	1.00828i	−0.999965	−	0.00831097i	$-0.997355\pi$
$19$	−4.39498	−	4.39498i	−1.00828	−	1.00828i	−0.00831097	−	0.999965i	$-0.502645\pi$
$20$	−0.874489	+	5.53324i	−0.195542	+	1.23727i
$21$		0			0
$22$	0.984999	−	1.93397i	0.210003	−	0.412323i
$23$	2.95135			0.615398			0.307699	−	0.951484i	$-0.400441\pi$
$23$	2.95135			0.615398			0.307699	+	0.951484i	$0.400441\pi$
$24$		0			0
$25$		−	2.84537i		−	0.569074i
$26$	−4.62699	+	2.14265i	−0.907427	+	0.420209i
$27$		0			0
$28$	−8.54727	−	1.35084i	−1.61528	−	0.255284i
$29$			6.96062i			1.29255i	0.763103	+	0.646277i	$0.223675\pi$
$29$			6.96062i			1.29255i	−0.763103	+	0.646277i	$0.776325\pi$
$30$		0			0
$31$	3.05943	−	3.05943i	0.549489	−	0.549489i	−0.376804	−	0.926293i	$-0.622977\pi$
$31$	3.05943	−	3.05943i	0.549489	−	0.549489i	0.926293	+	0.376804i	$0.122977\pi$
$32$	−0.00471188	−	5.65685i	−0.000832951	−	1.00000i
$33$		0			0
$34$	−2.49250	−	7.66677i	−0.427460	−	1.31484i
$35$	12.1189			2.04846
$36$		0			0
$37$	−5.14026	−	5.14026i	−0.845053	−	0.845053i	0.144458	−	0.989511i	$-0.453856\pi$
$37$	−5.14026	−	5.14026i	−0.845053	−	0.845053i	−0.989511	+	0.144458i	$0.953856\pi$
$38$	−7.83257	−	3.98925i	−1.27061	−	0.647142i
$39$		0			0
$40$	1.24323	+	7.82415i	0.196572	+	1.23711i
$41$	2.77963	+	2.77963i	0.434106	+	0.434106i	0.890022	−	0.455917i	$-0.150689\pi$
$41$	2.77963	+	2.77963i	0.434106	+	0.434106i	−0.455917	+	0.890022i	$0.650689\pi$
$42$		0			0
$43$		−	3.00392i		−	0.458093i	−0.973415	−	0.229046i	$-0.926439\pi$
$43$		−	3.00392i		−	0.458093i	0.973415	−	0.229046i	$-0.0735608\pi$
$44$	0.479142	−	3.03172i	0.0722333	−	0.457049i
$45$		0			0
$46$	3.96934	−	1.29045i	0.585247	−	0.190266i
$47$	−6.40146	−	6.40146i	−0.933749	−	0.933749i	0.0641887	−	0.997938i	$-0.479554\pi$
$47$	−6.40146	−	6.40146i	−0.933749	−	0.933749i	−0.997938	+	0.0641887i	$0.979554\pi$
$48$		0			0
$49$			11.7202i			1.67431i
$50$	−1.24411	−	3.82681i	−0.175944	−	0.541192i
$51$		0			0
$52$	−5.28610	+	4.90481i	−0.733050	+	0.680175i
$53$			4.28172i			0.588140i	0.955784	+	0.294070i	$0.0950099\pi$
$53$			4.28172i			0.588140i	−0.955784	+	0.294070i	$0.904990\pi$
$54$		0			0
$55$			4.29856i			0.579618i
$56$	−12.0861	+	1.92044i	−1.61507	+	0.256629i
$57$		0			0
$58$	3.04346	+	9.36150i	0.399626	+	1.22923i
$59$	−3.00033	+	3.00033i	−0.390610	+	0.390610i	−0.874905	−	0.484295i	$-0.839076\pi$
$59$	−3.00033	+	3.00033i	−0.390610	+	0.390610i	0.484295	+	0.874905i	$0.339076\pi$
$60$		0			0
$61$			1.13106i			0.144817i	0.997375	+	0.0724084i	$0.0230685\pi$
$61$			1.13106i			0.144817i	−0.997375	+	0.0724084i	$0.976932\pi$
$62$	2.77699	−	5.45240i	0.352678	−	0.692455i
$63$		0			0
$64$	−2.47974	−	7.60598i	−0.309967	−	0.950747i
$65$	6.24001	−	7.94053i	0.773978	−	0.984902i
$66$		0			0
$67$	7.39889	+	7.39889i	0.903918	+	0.903918i	0.995772	−	0.0918540i	$-0.0292793\pi$
$67$	7.39889	+	7.39889i	0.903918	+	0.903918i	−0.0918540	+	0.995772i	$0.529279\pi$
$68$	−6.70444	−	9.22140i	−0.813033	−	1.11826i
$69$		0			0
$70$	16.2989	−	5.29885i	1.94810	−	0.633334i
$71$	3.20281	−	3.20281i	0.380104	−	0.380104i	−0.491036	−	0.871139i	$-0.663382\pi$
$71$	3.20281	−	3.20281i	0.380104	−	0.380104i	0.871139	+	0.491036i	$0.163382\pi$
$72$		0			0
$73$	7.87480	−	7.87480i	0.921675	−	0.921675i	−0.0754728	−	0.997148i	$-0.524047\pi$
$73$	7.87480	−	7.87480i	0.921675	−	0.921675i	0.997148	+	0.0754728i	$0.0240466\pi$
$74$	−9.16078	−	4.66573i	−1.06492	−	0.542380i
$75$		0			0
$76$	−12.2785	−	1.94053i	−1.40844	−	0.222594i
$77$	−6.64004			−0.756703
$78$		0			0
$79$			4.46803i			0.502693i	0.967897	+	0.251347i	$0.0808734\pi$
$79$			4.46803i			0.502693i	−0.967897	+	0.251347i	$0.919127\pi$
$80$	5.09309	+	9.97930i	0.569424	+	1.11572i
$81$		0			0
$82$	4.95376	+	2.52303i	0.547051	+	0.278622i
$83$	9.78962	+	9.78962i	1.07455	+	1.07455i	0.996987	+	0.0775625i	$0.0247137\pi$
$83$	9.78962	+	9.78962i	1.07455	+	1.07455i	0.0775625	+	0.996987i	$0.475286\pi$
$84$		0			0
$85$	11.2903	+	11.2903i	1.22461	+	1.22461i
$86$	−1.31343	−	4.04004i	−0.141631	−	0.435649i
$87$		0			0
$88$	−0.681180	−	4.28693i	−0.0726140	−	0.456989i
$89$	−4.24001	+	4.24001i	−0.449440	+	0.449440i	−0.895168	−	0.445728i	$-0.852945\pi$
$89$	−4.24001	+	4.24001i	−0.449440	+	0.449440i	0.445728	+	0.895168i	$0.352945\pi$
$90$		0			0
$91$	12.2659	+	9.63903i	1.28581	+	1.01045i
$92$	4.77422	−	3.47111i	0.497747	−	0.361888i
$93$		0			0
$94$	−11.4085	−	5.81050i	−1.17669	−	0.599308i
$95$	17.4092			1.78614
$96$		0			0
$97$	−11.5753	−	11.5753i	−1.17530	−	1.17530i	−0.980929	−	0.194366i	$-0.937735\pi$
$97$	−11.5753	−	11.5753i	−1.17530	−	1.17530i	−0.194366	−	0.980929i	$-0.562265\pi$
$98$	5.12453	+	15.7627i	0.517655	+	1.59228i
$99$		0			0
$100$	−3.34647	−	4.60279i	−0.334647	−	0.460279i
$101$	5.67835			0.565017			0.282509	−	0.959265i	$-0.408833\pi$
$101$	5.67835			0.565017			0.282509	+	0.959265i	$0.408833\pi$
$102$		0			0
$103$	−1.20900			−0.119126			−0.0595630	−	0.998225i	$-0.518971\pi$
$103$	−1.20900			−0.119126			−0.0595630	+	0.998225i	$0.518971\pi$
$104$	−4.96482	+	8.90789i	−0.486841	+	0.873491i
$105$		0			0
$106$	1.87214	+	5.75859i	0.181838	+	0.559324i
$107$	11.6314			1.12445			0.562225	−	0.826984i	$-0.309945\pi$
$107$	11.6314			1.12445			0.562225	+	0.826984i	$0.309945\pi$
$108$		0			0
$109$	7.32910	−	7.32910i	0.702001	−	0.702001i	−0.262839	−	0.964840i	$-0.584659\pi$
$109$	7.32910	−	7.32910i	0.702001	−	0.702001i	0.964840	+	0.262839i	$0.0846588\pi$
$110$	1.87950	+	5.78124i	0.179204	+	0.551219i
$111$		0			0
$112$	−15.4152	+	7.86736i	−1.45660	+	0.743396i
$113$	−15.2598			−1.43552			−0.717760	−	0.696291i	$-0.754832\pi$
$113$	−15.2598			−1.43552			−0.717760	+	0.696291i	$0.754832\pi$
$114$		0			0
$115$	−5.84537	+	5.84537i	−0.545084	+	0.545084i
$116$	8.18645	+	11.2598i	0.760092	+	1.04544i
$117$		0			0
$118$	−2.72336	+	5.34709i	−0.250705	+	0.492239i
$119$	−17.4403	+	17.4403i	−1.59875	+	1.59875i
$120$		0			0
$121$			8.64478i			0.785889i
$122$	0.494543	+	1.52118i	0.0447738	+	0.137722i
$123$		0			0
$124$	1.35084	−	8.54727i	0.121309	−	0.767568i
$125$	−4.26741	−	4.26741i	−0.381689	−	0.381689i
$126$		0			0
$127$	5.22910			0.464008			0.232004	−	0.972715i	$-0.425472\pi$
$127$	5.22910			0.464008			0.232004	+	0.972715i	$0.425472\pi$
$128$	−6.66070	−	9.14522i	−0.588728	−	0.808331i
$129$		0			0
$130$	4.92042	−	13.4078i	0.431550	−	1.17594i
$131$	−17.2100			−1.50364			−0.751821	−	0.659367i	$-0.770824\pi$
$131$	−17.2100			−1.50364			−0.751821	+	0.659367i	$0.770824\pi$
$132$		0			0
$133$			26.8922i			2.33185i
$134$	13.1860	+	6.71586i	1.13910	+	0.580162i
$135$		0			0
$136$	−13.0489	−	9.47064i	−1.11894	−	0.812101i
$137$	−2.23218	+	2.23218i	−0.190708	+	0.190708i	−0.796002	−	0.605294i	$-0.793056\pi$
$137$	−2.23218	+	2.23218i	−0.190708	+	0.190708i	0.605294	+	0.796002i	$0.293056\pi$
$138$		0			0
$139$	16.1346			1.36852			0.684259	−	0.729239i	$-0.260126\pi$
$139$	16.1346			1.36852			0.684259	+	0.729239i	$0.260126\pi$
$140$	19.6040	−	14.2531i	1.65684	−	1.20461i
$141$		0			0
$142$	2.90714	−	5.70793i	0.243962	−	0.478999i
$143$	−3.41897	+	4.35070i	−0.285908	+	0.363824i
$144$		0			0
$145$	−13.7860	−	13.7860i	−1.14487	−	1.14487i
$146$	7.14783	−	14.0342i	0.591558	−	1.16148i
$147$		0			0
$148$	−14.3606	−	2.26959i	−1.18043	−	0.186559i
$149$	9.30975	−	9.30975i	0.762684	−	0.762684i	−0.214123	−	0.976807i	$-0.568689\pi$
$149$	9.30975	−	9.30975i	0.762684	−	0.762684i	0.976807	+	0.214123i	$0.0686893\pi$
$150$		0			0
$151$	−6.21009	−	6.21009i	−0.505370	−	0.505370i	0.407732	−	0.913102i	$-0.366320\pi$
$151$	−6.21009	−	6.21009i	−0.505370	−	0.505370i	−0.913102	+	0.407732i	$0.866320\pi$
$152$	−17.3621	+	2.75878i	−1.40825	+	0.223767i
$153$		0			0
$154$	−8.93036	+	2.90329i	−0.719629	+	0.233954i
$155$			12.1189i			0.973410i
$156$		0			0
$157$		−	13.0048i		−	1.03789i	−0.854807	−	0.518947i	$-0.826324\pi$
$157$		−	13.0048i		−	1.03789i	0.854807	−	0.518947i	$-0.173676\pi$
$158$	1.95360	+	6.00917i	0.155420	+	0.478064i
$159$		0			0
$160$	11.2132	+	11.1945i	0.886478	+	0.885003i
$161$	−9.02943	−	9.02943i	−0.711618	−	0.711618i
$162$		0			0
$163$	4.16037	−	4.16037i	0.325865	−	0.325865i	−0.525146	−	0.851012i	$-0.675989\pi$
$163$	4.16037	−	4.16037i	0.325865	−	0.325865i	0.851012	+	0.525146i	$0.175989\pi$
$164$	7.76560	+	1.22730i	0.606392	+	0.0958359i
$165$		0			0
$166$	17.4467	+	8.88588i	1.35413	+	0.689678i
$167$	9.56896	+	9.56896i	0.740469	+	0.740469i	0.972668	−	0.232199i	$-0.0745922\pi$
$167$	9.56896	+	9.56896i	0.740469	+	0.740469i	−0.232199	+	0.972668i	$0.574592\pi$
$168$		0			0
$169$	12.6314	−	3.07370i	0.971646	−	0.236439i
$170$	20.1212	+	10.2480i	1.54323	+	0.785989i
$171$		0			0
$172$	−3.53293	−	4.85926i	−0.269384	−	0.370515i
$173$	10.9034			0.828968			0.414484	−	0.910057i	$-0.363962\pi$
$173$	10.9034			0.828968			0.414484	+	0.910057i	$0.363962\pi$
$174$		0			0
$175$	−8.70520	+	8.70520i	−0.658051	+	0.658051i
$176$	−2.79055	−	5.46776i	−0.210346	−	0.412148i
$177$		0			0
$178$	−3.84859	+	7.55640i	−0.288464	+	0.566376i
$179$		−	6.70998i		−	0.501527i	−0.968048	−	0.250764i	$-0.919318\pi$
$179$		−	6.70998i		−	0.501527i	0.968048	−	0.250764i	$-0.0806817\pi$
$180$		0			0
$181$	−15.8485			−1.17801			−0.589003	−	0.808131i	$-0.700479\pi$
$181$	−15.8485			−1.17801			−0.589003	+	0.808131i	$0.700479\pi$
$182$	20.7112	+	7.60065i	1.53522	+	0.563397i
$183$		0			0
$184$	4.90326	−	6.75586i	0.361473	−	0.498048i
$185$	20.3614			1.49700
$186$		0			0
$187$	−6.18608	−	6.18608i	−0.452371	−	0.452371i
$188$	−17.8841	−	2.82645i	−1.30433	−	0.206140i
$189$		0			0
$190$	23.4140	−	7.61199i	1.69863	−	0.552232i
$191$		−	17.4715i		−	1.26419i	−0.774890	−	0.632096i	$-0.782195\pi$
$191$		−	17.4715i		−	1.26419i	0.774890	−	0.632096i	$-0.217805\pi$
$192$		0			0
$193$	12.6490	−	12.6490i	0.910496	−	0.910496i	−0.0858148	−	0.996311i	$-0.527349\pi$
$193$	12.6490	−	12.6490i	0.910496	−	0.910496i	0.996311	+	0.0858148i	$0.0273493\pi$
$194$	−20.6291	−	10.5067i	−1.48108	−	0.754339i
$195$		0			0
$196$	13.7842	+	18.9590i	0.984586	+	1.35422i
$197$	−4.24269	+	4.24269i	−0.302279	+	0.302279i	−0.841905	−	0.539626i	$-0.818566\pi$
$197$	−4.24269	+	4.24269i	−0.302279	+	0.302279i	0.539626	+	0.841905i	$0.318566\pi$
$198$		0			0
$199$	8.86969			0.628755			0.314378	−	0.949298i	$-0.398204\pi$
$199$	8.86969			0.628755			0.314378	+	0.949298i	$0.398204\pi$
$200$	−6.51327	−	4.72719i	−0.460558	−	0.334263i
$201$		0			0
$202$	7.63695	−	2.48280i	0.537334	−	0.174689i
$203$	21.2955	−	21.2955i	1.49465	−	1.49465i
$204$		0			0
$205$	−11.0105			−0.769010
$206$	−1.62601	+	0.528622i	−0.113289	+	0.0368308i
$207$		0			0
$208$	−2.78242	+	14.1513i	−0.192926	+	0.981213i
$209$	−9.53866			−0.659803
$210$		0			0
$211$	8.48028			0.583807			0.291903	−	0.956448i	$-0.405711\pi$
$211$	8.48028			0.583807			0.291903	+	0.956448i	$0.405711\pi$
$212$	5.03578	+	6.92630i	0.345859	+	0.475700i
$213$		0			0
$214$	15.6434	−	5.08572i	1.06936	−	0.347652i
$215$	5.94949	+	5.94949i	0.405752	+	0.405752i
$216$		0			0
$217$	−18.7202			−1.27081
$218$	6.65251	−	13.0617i	0.450565	−	0.884647i
$219$		0			0
$220$	5.05558	+	6.95353i	0.340847	+	0.468807i
$221$	2.44723	+	20.4073i	0.164619	+	1.37274i
$222$		0			0
$223$	16.9807	−	16.9807i	1.13711	−	1.13711i	0.148143	−	0.988966i	$-0.452670\pi$
$223$	16.9807	−	16.9807i	1.13711	−	1.13711i	0.988966	−	0.148143i	$-0.0473295\pi$
$224$	−17.2923	+	17.3211i	−1.15539	+	1.15732i
$225$		0			0
$226$	−20.5233	+	6.67219i	−1.36519	+	0.443827i
$227$	−8.63107	−	8.63107i	−0.572864	−	0.572864i	0.360064	−	0.932928i	$-0.382755\pi$
$227$	−8.63107	−	8.63107i	−0.572864	−	0.572864i	−0.932928	+	0.360064i	$0.882755\pi$
$228$		0			0
$229$	4.16041	+	4.16041i	0.274928	+	0.274928i	0.831080	−	0.556153i	$-0.187723\pi$
$229$	4.16041	+	4.16041i	0.274928	+	0.274928i	−0.556153	+	0.831080i	$0.687723\pi$
$230$	−5.30575	+	10.4174i	−0.349851	+	0.686904i
$231$		0			0
$232$	15.9334	+	11.5641i	1.04608	+	0.759221i
$233$			2.78928i			0.182732i	0.995817	+	0.0913660i	$0.0291233\pi$
$233$			2.78928i			0.182732i	−0.995817	+	0.0913660i	$0.970877\pi$
$234$		0			0
$235$	25.3572			1.65412
$236$	−1.32475	+	8.38219i	−0.0862336	+	0.545634i
$237$		0			0
$238$	−15.8303	+	31.0815i	−1.02613	+	2.01472i
$239$	−3.17166	+	3.17166i	−0.205158	+	0.205158i	−0.802206	−	0.597048i	$-0.796340\pi$
$239$	−3.17166	+	3.17166i	−0.205158	+	0.205158i	0.597048	+	0.802206i	$0.296340\pi$
$240$		0			0
$241$	−19.8233	+	19.8233i	−1.27693	+	1.27693i	−0.334554	+	0.942377i	$0.608586\pi$
$241$	−19.8233	+	19.8233i	−1.27693	+	1.27693i	−0.942377	+	0.334554i	$0.891414\pi$
$242$	3.77984	+	11.6266i	0.242977	+	0.747384i
$243$		0			0
$244$	1.33025	+	1.82964i	0.0851602	+	0.117131i
$245$	−23.2127	−	23.2127i	−1.48300	−	1.48300i
$246$		0			0
$247$	17.6203	+	13.8468i	1.12116	+	0.881052i
$248$	−1.92044	−	12.0861i	−0.121948	−	0.767467i
$249$		0			0
$250$	−7.60523	−	3.87346i	−0.480997	−	0.244979i
$251$			5.23069i			0.330158i	0.986280	+	0.165079i	$0.0527879\pi$
$251$			5.23069i			0.330158i	−0.986280	+	0.165079i	$0.947212\pi$
$252$		0			0
$253$	3.20274	−	3.20274i	0.201354	−	0.201354i
$254$	7.03275	−	2.28637i	0.441274	−	0.143460i
$255$		0			0
$256$	−12.9568	−	9.38730i	−0.809800	−	0.586707i
$257$			8.93669i			0.557455i	0.960370	+	0.278728i	$0.0899127\pi$
$257$			8.93669i			0.557455i	−0.960370	+	0.278728i	$0.910087\pi$
$258$		0			0
$259$			31.4525i			1.95436i
$260$	0.755169	−	20.1839i	0.0468336	−	1.25175i
$261$		0			0
$262$	−23.1461	+	7.52489i	−1.42997	+	0.464889i
$263$		−	6.37699i		−	0.393222i	−0.980482	−	0.196611i	$-0.937006\pi$
$263$		−	6.37699i		−	0.393222i	0.980482	−	0.196611i	$-0.0629936\pi$
$264$		0			0
$265$	−8.48028	−	8.48028i	−0.520940	−	0.520940i
$266$	11.7583	+	36.1680i	0.720950	+	2.21760i
$267$		0			0
$268$	20.6707	+	3.26685i	1.26266	+	0.199555i
$269$			15.2813i			0.931717i	0.884859	+	0.465859i	$0.154255\pi$
$269$			15.2813i			0.931717i	−0.884859	+	0.465859i	$0.845745\pi$
$270$		0			0
$271$	1.94520	+	1.94520i	0.118163	+	0.118163i	0.763716	−	0.645553i	$-0.223373\pi$
$271$	1.94520	+	1.94520i	0.118163	+	0.118163i	−0.645553	+	0.763716i	$0.723373\pi$
$272$	−21.6908	−	7.03178i	−1.31520	−	0.426364i
$273$		0			0
$274$	−2.02611	+	3.97811i	−0.122402	+	0.240326i
$275$	−3.08773	−	3.08773i	−0.186197	−	0.186197i
$276$		0			0
$277$	6.63729			0.398796			0.199398	−	0.979919i	$-0.436101\pi$
$277$	6.63729			0.398796			0.199398	+	0.979919i	$0.436101\pi$
$278$	21.6998	−	7.05469i	1.30147	−	0.423112i
$279$		0			0
$280$	20.1338	−	27.7410i	1.20323	−	1.65784i
$281$	13.3992	−	13.3992i	0.799331	−	0.799331i	−0.183659	−	0.982990i	$-0.558794\pi$
$281$	13.3992	−	13.3992i	0.799331	−	0.799331i	0.982990	+	0.183659i	$0.0587943\pi$
$282$		0			0
$283$		−	8.82007i		−	0.524299i	−0.965027	−	0.262149i	$-0.915569\pi$
$283$		−	8.82007i		−	0.524299i	0.965027	−	0.262149i	$-0.0844313\pi$
$284$	1.41415	−	8.94786i	0.0839141	−	0.530958i
$285$		0			0
$286$	−2.69595	+	7.34627i	−0.159415	+	0.434394i
$287$		−	17.0082i		−	1.00396i
$288$		0			0
$289$	−15.4959			−0.911526
$290$	−24.5690	−	12.5134i	−1.44274	−	0.734810i
$291$		0			0
$292$	3.47698	−	22.0002i	0.203475	−	1.28747i
$293$	−12.6596	−	12.6596i	−0.739582	−	0.739582i	0.232915	−	0.972497i	$-0.425174\pi$
$293$	−12.6596	−	12.6596i	−0.739582	−	0.739582i	−0.972497	+	0.232915i	$0.925174\pi$
$294$		0			0
$295$		−	11.8848i		−	0.691959i
$296$	−20.3063	+	3.22660i	−1.18028	+	0.187542i
$297$		0			0
$298$	8.45031	−	16.5915i	0.489513	−	0.961120i
$299$	−10.5655	+	1.26701i	−0.611021	+	0.0732732i
$300$		0			0
$301$	−9.19026	+	9.19026i	−0.529718	+	0.529718i
$302$	−11.0674	−	5.63680i	−0.636858	−	0.324362i
$303$		0			0
$304$	−22.1444	+	11.3017i	−1.27007	+	0.648200i
$305$	−2.24014	−	2.24014i	−0.128270	−	0.128270i
$306$		0			0
$307$	−11.6407	+	11.6407i	−0.664371	+	0.664371i	−0.956407	−	0.292036i	$-0.905667\pi$
$307$	−11.6407	+	11.6407i	−0.664371	+	0.664371i	0.292036	+	0.956407i	$0.405667\pi$
$308$	−10.7412	+	7.80942i	−0.612038	+	0.444983i
$309$		0			0
$310$	5.29885	+	16.2989i	0.300954	+	0.925718i
$311$	14.2715			0.809263			0.404632	−	0.914480i	$-0.367400\pi$
$311$	14.2715			0.809263			0.404632	+	0.914480i	$0.367400\pi$
$312$		0			0
$313$	−20.4770			−1.15743			−0.578714	−	0.815531i	$-0.696445\pi$
$313$	−20.4770			−1.15743			−0.578714	+	0.815531i	$0.696445\pi$
$314$	−5.68620	−	17.4904i	−0.320891	−	0.987042i
$315$		0			0
$316$	5.25490	+	7.22768i	0.295611	+	0.406589i
$317$	18.4519	−	18.4519i	1.03636	−	1.03636i	0.0370478	−	0.999313i	$-0.488205\pi$
$317$	18.4519	−	18.4519i	1.03636	−	1.03636i	0.999313	−	0.0370478i	$-0.0117954\pi$
$318$		0			0
$319$	7.55351	+	7.55351i	0.422915	+	0.422915i
$320$	19.9755	+	10.1529i	1.11667	+	0.567565i
$321$		0			0
$322$	−16.0919	−	8.19587i	−0.896768	−	0.456738i
$323$	−25.0537	+	25.0537i	−1.39402	+	1.39402i
$324$		0			0
$325$	1.22152	+	10.1861i	0.0677575	+	0.565026i
$326$	3.77630	−	7.41447i	0.209150	−	0.410649i
$327$		0			0
$328$	10.9808	−	1.74481i	0.606312	−	0.0963410i
$329$			39.1696i			2.15949i
$330$		0			0
$331$	−9.99851	−	9.99851i	−0.549568	−	0.549568i	0.376748	−	0.926316i	$-0.377042\pi$
$331$	−9.99851	−	9.99851i	−0.549568	−	0.549568i	−0.926316	+	0.376748i	$0.877042\pi$
$332$	27.3498	+	4.32244i	1.50101	+	0.237224i
$333$		0			0
$334$	17.0535	+	8.68560i	0.933124	+	0.475255i
$335$	−29.3081			−1.60128
$336$		0			0
$337$		−	13.7956i		−	0.751492i	−0.926723	−	0.375746i	$-0.877387\pi$
$337$		−	13.7956i		−	0.751492i	0.926723	−	0.375746i	$-0.122613\pi$
$338$	15.6443	−	9.65685i	0.850940	−	0.525263i
$339$		0			0
$340$	31.5424	+	4.98505i	1.71062	+	0.270352i
$341$		−	6.64004i		−	0.359579i
$342$		0			0
$343$	14.4410	−	14.4410i	0.779740	−	0.779740i
$344$	−6.87619	−	4.99060i	−0.370739	−	0.269075i
$345$		0			0
$346$	14.6642	−	4.76739i	0.788353	−	0.256296i
$347$	−2.33288			−0.125236			−0.0626178	−	0.998038i	$-0.519945\pi$
$347$	−2.33288			−0.125236			−0.0626178	+	0.998038i	$0.519945\pi$
$348$		0			0
$349$	−14.8829	−	14.8829i	−0.796661	−	0.796661i	0.185906	−	0.982567i	$-0.440478\pi$
$349$	−14.8829	−	14.8829i	−0.796661	−	0.796661i	−0.982567	+	0.185906i	$0.940478\pi$
$350$	−7.90157	+	15.5141i	−0.422357	+	0.829263i
$351$		0			0
$352$	−6.14381	−	6.13358i	−0.327466	−	0.326921i
$353$	3.75999	+	3.75999i	0.200124	+	0.200124i	0.800053	−	0.599929i	$-0.204805\pi$
$353$	3.75999	+	3.75999i	0.200124	+	0.200124i	−0.599929	+	0.800053i	$0.704805\pi$
$354$		0			0
$355$			12.6868i			0.673347i
$356$	−1.87210	+	11.8455i	−0.0992213	+	0.627812i
$357$		0			0
$358$	−2.93387	−	9.02441i	−0.155060	−	0.476955i
$359$	17.6464	+	17.6464i	0.931343	+	0.931343i	0.997790	−	0.0664468i	$-0.0211663\pi$
$359$	17.6464	+	17.6464i	0.931343	+	0.931343i	−0.0664468	+	0.997790i	$0.521166\pi$
$360$		0			0
$361$			19.6316i			1.03324i
$362$	−21.3150	+	6.92958i	−1.12029	+	0.364211i
$363$		0			0
$364$	31.1783	+	1.16652i	1.63419	+	0.0611423i
$365$			31.1933i			1.63273i
$366$		0			0
$367$		−	37.0651i		−	1.93478i	−0.253290	−	0.967390i	$-0.581513\pi$
$367$		−	37.0651i		−	1.93478i	0.253290	−	0.967390i	$-0.418487\pi$
$368$	3.64058	−	11.2300i	0.189779	−	0.585405i
$369$		0			0
$370$	27.3845	−	8.90280i	1.42365	−	0.462834i
$371$	13.0996	−	13.0996i	0.680098	−	0.680098i
$372$		0			0
$373$			17.1978i			0.890470i	0.895414	+	0.445235i	$0.146880\pi$
$373$			17.1978i			0.890470i	−0.895414	+	0.445235i	$0.853120\pi$
$374$	−11.0246	−	5.61501i	−0.570069	−	0.290345i
$375$		0			0
$376$	−25.2886	+	4.01828i	−1.30416	+	0.207227i
$377$	−2.98819	−	24.9183i	−0.153900	−	1.28336i
$378$		0			0
$379$	−20.6610	−	20.6610i	−1.06129	−	1.06129i	−0.997995	−	0.0632908i	$-0.979840\pi$
$379$	−20.6610	−	20.6610i	−1.06129	−	1.06129i	−0.0632908	−	0.997995i	$-0.520160\pi$
$380$	28.1618	−	20.4751i	1.44467	−	1.05035i
$381$		0			0
$382$	−7.63923	−	23.4978i	−0.390857	−	1.20225i
$383$	14.2843	−	14.2843i	0.729894	−	0.729894i	−0.240705	−	0.970598i	$-0.577379\pi$
$383$	14.2843	−	14.2843i	0.729894	−	0.729894i	0.970598	+	0.240705i	$0.0773785\pi$
$384$		0			0
$385$	13.1511	−	13.1511i	0.670243	−	0.670243i
$386$	11.4813	−	22.5426i	0.584383	−	1.14739i
$387$		0			0
$388$	−32.3386	−	5.11088i	−1.64174	−	0.259466i
$389$	3.02809			0.153530			0.0767651	−	0.997049i	$-0.475541\pi$
$389$	3.02809			0.153530			0.0767651	+	0.997049i	$0.475541\pi$
$390$		0			0
$391$		−	16.8242i		−	0.850837i
$392$	26.8284	+	19.4715i	1.35504	+	0.983457i
$393$		0			0
$394$	−3.85102	+	7.56117i	−0.194012	+	0.380926i
$395$	−8.84929	−	8.84929i	−0.445256	−	0.445256i
$396$		0			0
$397$	5.46083	+	5.46083i	0.274071	+	0.274071i	0.830737	−	0.556666i	$-0.187920\pi$
$397$	5.46083	+	5.46083i	0.274071	+	0.274071i	−0.556666	+	0.830737i	$0.687920\pi$
$398$	11.9291	−	3.87818i	0.597950	−	0.194396i
$399$		0			0
$400$	−10.8268	−	3.50986i	−0.541339	−	0.175493i
$401$	14.1868	−	14.1868i	0.708456	−	0.708456i	−0.257754	−	0.966210i	$-0.582983\pi$
$401$	14.1868	−	14.1868i	0.708456	−	0.708456i	0.966210	+	0.257754i	$0.0829826\pi$
$402$		0			0
$403$	−9.63903	+	12.2659i	−0.480154	+	0.611006i
$404$	9.18554	−	6.67836i	0.456998	−	0.332261i
$405$		0			0
$406$	19.3296	−	37.9520i	0.959310	−	1.88353i
$407$	−11.1562			−0.552992
$408$		0			0
$409$	−9.80736	−	9.80736i	−0.484943	−	0.484943i	0.421763	−	0.906706i	$-0.361411\pi$
$409$	−9.80736	−	9.80736i	−0.484943	−	0.484943i	−0.906706	+	0.421763i	$0.861411\pi$
$410$	−14.8084	+	4.81425i	−0.731332	+	0.237759i
$411$		0			0
$412$	−1.95572	+	1.42191i	−0.0963516	+	0.0700526i
$413$	18.3586			0.903367
$414$		0			0
$415$	−38.7782			−1.90355
$416$	2.44535	+	20.2490i	0.119893	+	0.992787i
$417$		0			0
$418$	−12.8288	+	4.17069i	−0.627476	+	0.203995i
$419$	−17.4997			−0.854915			−0.427457	−	0.904036i	$-0.640591\pi$
$419$	−17.4997			−0.854915			−0.427457	+	0.904036i	$0.640591\pi$
$420$		0			0
$421$	−11.9652	+	11.9652i	−0.583147	+	0.583147i	−0.935767	−	0.352620i	$-0.885291\pi$
$421$	−11.9652	+	11.9652i	−0.583147	+	0.583147i	0.352620	+	0.935767i	$0.385291\pi$
$422$	11.4053	−	3.70792i	0.555203	−	0.180499i
$423$		0			0
$424$	9.80119	+	7.11350i	0.475988	+	0.345462i
$425$	−16.2201			−0.786790
$426$		0			0
$427$	3.46038	−	3.46038i	0.167460	−	0.167460i
$428$	18.8154	−	13.6798i	0.909479	−	0.661238i
$429$		0			0
$430$	10.6030	+	5.40026i	0.511320	+	0.260423i
$431$	0.239905	−	0.239905i	0.0115558	−	0.0115558i	−0.701305	−	0.712861i	$-0.747399\pi$
$431$	0.239905	−	0.239905i	0.0115558	−	0.0115558i	0.712861	+	0.701305i	$0.247399\pi$
$432$		0			0
$433$		−	20.0909i		−	0.965507i	−0.875756	−	0.482754i	$-0.839637\pi$
$433$		−	20.0909i		−	0.965507i	0.875756	−	0.482754i	$-0.160363\pi$
$434$	−25.1772	+	8.18521i	−1.20854	+	0.392902i
$435$		0			0
$436$	3.23604	−	20.4757i	0.154978	−	0.980608i
$437$	−12.9711	−	12.9711i	−0.620492	−	0.620492i
$438$		0			0
$439$	2.49150			0.118913			0.0594565	−	0.998231i	$-0.481063\pi$
$439$	2.49150			0.118913			0.0594565	+	0.998231i	$0.481063\pi$
$440$	9.83973	+	7.14147i	0.469091	+	0.340456i
$441$		0			0
$442$	12.2142	+	26.3763i	0.580972	+	1.25459i
$443$	−13.5192			−0.642318			−0.321159	−	0.947025i	$-0.604072\pi$
$443$	−13.5192			−0.642318			−0.321159	+	0.947025i	$0.604072\pi$
$444$		0			0
$445$		−	16.7953i		−	0.796175i
$446$	15.4131	−	30.2623i	0.729830	−	1.43296i
$447$		0			0
$448$	−15.6833	+	30.8565i	−0.740968	+	1.45783i
$449$	−12.8287	+	12.8287i	−0.605424	+	0.605424i	−0.941747	−	0.336323i	$-0.890817\pi$
$449$	−12.8287	+	12.8287i	−0.605424	+	0.605424i	0.336323	+	0.941747i	$0.390817\pi$
$450$		0			0
$451$	6.03279			0.284073
$452$	−24.6849	+	17.9472i	−1.16108	+	0.844164i
$453$		0			0
$454$	−15.3820	−	7.83429i	−0.721912	−	0.367681i
$455$	−43.3843	+	5.20262i	−2.03389	+	0.243903i
$456$		0			0
$457$	21.9620	+	21.9620i	1.02734	+	1.02734i	0.999616	+	0.0277231i	$0.00882568\pi$
$457$	21.9620	+	21.9620i	1.02734	+	1.02734i	0.0277231	+	0.999616i	$0.491174\pi$
$458$	7.41453	+	3.77634i	0.346458	+	0.176457i
$459$		0			0
$460$	−2.58092	+	16.3305i	−0.120336	+	0.761414i
$461$	−20.6299	+	20.6299i	−0.960830	+	0.960830i	−0.999261	−	0.0384313i	$-0.987764\pi$
$461$	−20.6299	+	20.6299i	−0.960830	+	0.960830i	0.0384313	+	0.999261i	$0.487764\pi$
$462$		0			0
$463$	0.0796856	+	0.0796856i	0.00370330	+	0.00370330i	0.708956	−	0.705253i	$-0.249166\pi$
$463$	0.0796856	+	0.0796856i	0.00370330	+	0.00370330i	−0.705253	+	0.708956i	$0.749166\pi$
$464$	26.4855	+	8.58615i	1.22956	+	0.398602i
$465$		0			0
$466$	1.21959	+	3.75137i	0.0564962	+	0.173779i
$467$			21.9896i			1.01756i	0.860898	+	0.508778i	$0.169903\pi$
$467$			21.9896i			1.01756i	−0.860898	+	0.508778i	$0.830097\pi$
$468$		0			0
$469$		−	45.2727i		−	2.09050i
$470$	34.1035	−	11.0872i	1.57308	−	0.511413i
$471$		0			0
$472$	1.88335	+	11.8526i	0.0866880	+	0.545562i
$473$	−3.25979	−	3.25979i	−0.149885	−	0.149885i
$474$		0			0
$475$	−12.5053	+	12.5053i	−0.573784	+	0.573784i
$476$	−7.70047	+	48.7239i	−0.352951	+	2.23326i
$477$		0			0
$478$	−2.87887	+	5.65242i	−0.131676	+	0.258536i
$479$	−4.31955	−	4.31955i	−0.197365	−	0.197365i	0.601504	−	0.798870i	$-0.294568\pi$
$479$	−4.31955	−	4.31955i	−0.197365	−	0.197365i	−0.798870	+	0.601504i	$0.794568\pi$
$480$		0			0
$481$	20.6083	+	16.1949i	0.939659	+	0.738424i
$482$	−17.9933	+	35.3284i	−0.819572	+	1.60916i
$483$		0			0
$484$	10.1672	+	13.9842i	0.462146	+	0.635643i
$485$	45.8516			2.08201
$486$		0			0
$487$	−28.5902	+	28.5902i	−1.29555	+	1.29555i	−0.364243	+	0.931304i	$0.618672\pi$
$487$	−28.5902	+	28.5902i	−1.29555	+	1.29555i	−0.931304	+	0.364243i	$0.881328\pi$
$488$	2.58907	+	1.87909i	0.117202	+	0.0850626i
$489$		0			0
$490$	−41.3688	−	21.0698i	−1.86885	−	0.951836i
$491$		−	12.4888i		−	0.563611i	−0.959472	−	0.281805i	$-0.909067\pi$
$491$		−	12.4888i		−	0.563611i	0.959472	−	0.281805i	$-0.0909333\pi$
$492$		0			0
$493$	39.6791			1.78706
$494$	29.7524	+	10.9186i	1.33862	+	0.491251i
$495$		0			0
$496$	−7.86736	−	15.4152i	−0.353255	−	0.692161i
$497$	−19.5975			−0.879069
$498$		0			0
$499$	10.2871	+	10.2871i	0.460512	+	0.460512i	0.898823	−	0.438311i	$-0.144423\pi$
$499$	10.2871	+	10.2871i	0.460512	+	0.460512i	−0.438311	+	0.898823i	$0.644423\pi$
$500$	−11.9221	−	1.88420i	−0.533172	−	0.0842640i
$501$		0			0
$502$	2.28707	+	7.03488i	0.102077	+	0.313982i
$503$		−	20.3269i		−	0.906329i	−0.891427	−	0.453165i	$-0.850295\pi$
$503$		−	20.3269i		−	0.906329i	0.891427	−	0.453165i	$-0.149705\pi$
$504$		0			0
$505$	−11.2464	+	11.2464i	−0.500459	+	0.500459i
$506$	2.90707	−	5.70781i	0.129235	−	0.253743i
$507$		0			0
$508$	8.45882	−	6.15000i	0.375299	−	0.272862i
$509$	−2.36729	+	2.36729i	−0.104928	+	0.104928i	−0.757622	−	0.652694i	$-0.773639\pi$
$509$	−2.36729	+	2.36729i	−0.104928	+	0.104928i	0.652694	+	0.757622i	$0.273639\pi$
$510$		0			0
$511$	−48.1847			−2.13157
$512$	−21.5304	−	6.95998i	−0.951519	−	0.307591i
$513$		0			0
$514$	3.90748	+	12.0192i	0.172351	+	0.530143i
$515$	2.39451	−	2.39451i	0.105515	−	0.105515i
$516$		0			0
$517$	−13.8935			−0.611033
$518$	13.7523	+	42.3012i	0.604240	+	1.85861i
$519$		0			0
$520$	−7.80956	−	27.4760i	−0.342472	−	1.20490i
$521$	25.2723			1.10720			0.553600	−	0.832782i	$-0.313254\pi$
$521$	25.2723			1.10720			0.553600	+	0.832782i	$0.313254\pi$
$522$		0			0
$523$	−14.5946			−0.638178			−0.319089	−	0.947725i	$-0.603377\pi$
$523$	−14.5946			−0.638178			−0.319089	+	0.947725i	$0.603377\pi$
$524$	−27.8396	+	20.2408i	−1.21618	+	0.884224i
$525$		0			0
$526$	−2.78828	−	8.57657i	−0.121575	−	0.373956i
$527$	−17.4403	−	17.4403i	−0.759712	−	0.759712i
$528$		0			0
$529$	−14.2896			−0.621285
$530$	−15.1133	−	7.69742i	−0.656478	−	0.334355i
$531$		0			0
$532$	31.6282	+	43.5019i	1.37125	+	1.88605i
$533$	−11.1441	−	8.75752i	−0.482705	−	0.379330i
$534$		0			0
$535$	−23.0369	+	23.0369i	−0.995972	+	0.995972i
$536$	29.2289	−	4.64437i	1.26250	−	0.200606i
$537$		0			0
$538$	6.68160	+	20.5522i	0.288064	+	0.886068i
$539$	12.7185	+	12.7185i	0.547823	+	0.547823i
$540$		0			0
$541$	−0.0297801	−	0.0297801i	−0.00128035	−	0.00128035i	0.706466	−	0.707747i	$-0.250288\pi$
$541$	−0.0297801	−	0.0297801i	−0.00128035	−	0.00128035i	−0.707747	+	0.706466i	$0.750288\pi$
$542$	3.46667	+	1.76563i	0.148906	+	0.0758403i
$543$		0			0
$544$	−32.2470	+	0.0268602i	−1.38258	+	0.00115162i
$545$			29.0317i			1.24358i
$546$		0			0
$547$	8.90794			0.380876			0.190438	−	0.981699i	$-0.439009\pi$
$547$	8.90794			0.380876			0.190438	+	0.981699i	$0.439009\pi$
$548$	−0.985580	+	6.23615i	−0.0421019	+	0.266395i
$549$		0			0
$550$	−5.50285	−	2.80269i	−0.234642	−	0.119507i
$551$	30.5917	−	30.5917i	1.30325	−	1.30325i
$552$		0			0
$553$	13.6696	−	13.6696i	0.581291	−	0.581291i
$554$	8.92665	−	2.90209i	0.379257	−	0.123298i
$555$		0			0
$556$	26.1000	−	18.9760i	1.10689	−	0.804763i
$557$	−3.04221	−	3.04221i	−0.128902	−	0.128902i	0.639712	−	0.768615i	$-0.279054\pi$
$557$	−3.04221	−	3.04221i	−0.128902	−	0.128902i	−0.768615	+	0.639712i	$0.779054\pi$
$558$		0			0
$559$	1.28958	+	10.7537i	0.0545434	+	0.454834i
$560$	14.9490	−	46.1128i	0.631711	−	1.94862i
$561$		0			0
$562$	12.1623	−	23.8796i	0.513034	−	1.00730i
$563$			19.1221i			0.805900i	0.915222	+	0.402950i	$0.132015\pi$
$563$			19.1221i			0.805900i	−0.915222	+	0.402950i	$0.867985\pi$
$564$		0			0
$565$	30.2232	−	30.2232i	1.27150	−	1.27150i
$566$	−3.85649	−	11.8623i	−0.162100	−	0.498611i
$567$		0			0
$568$	−2.01044	−	12.6525i	−0.0843563	−	0.530887i
$569$			17.6181i			0.738590i	0.929312	+	0.369295i	$0.120401\pi$
$569$			17.6181i			0.738590i	−0.929312	+	0.369295i	$0.879599\pi$
$570$		0			0
$571$			3.59788i			0.150567i	0.997162	+	0.0752833i	$0.0239861\pi$
$571$			3.59788i			0.150567i	−0.997162	+	0.0752833i	$0.976014\pi$
$572$	−0.413765	+	11.0590i	−0.0173004	+	0.462398i
$573$		0			0
$574$	−7.43665	−	22.8747i	−0.310400	−	0.954770i
$575$		−	8.39767i		−	0.350207i
$576$		0			0
$577$	26.9842	+	26.9842i	1.12337	+	1.12337i	0.991232	+	0.132135i	$0.0421832\pi$
$577$	26.9842	+	26.9842i	1.12337	+	1.12337i	0.132135	+	0.991232i	$0.457817\pi$
$578$	−20.8409	+	6.77545i	−0.866866	+	0.281822i
$579$		0			0
$580$	−38.5148	−	6.08698i	−1.59924	−	0.252748i
$581$		−	59.9012i		−	2.48512i
$582$		0			0
$583$	4.64644	+	4.64644i	0.192436	+	0.192436i
$584$	−4.94311	−	31.1089i	−0.204547	−	1.28730i
$585$		0			0
$586$	−22.5615	−	11.4909i	−0.932007	−	0.474686i
$587$	−15.2640	−	15.2640i	−0.630014	−	0.630014i	0.318057	−	0.948071i	$-0.396970\pi$
$587$	−15.2640	−	15.2640i	−0.630014	−	0.630014i	−0.948071	+	0.318057i	$0.896970\pi$
$588$		0			0
$589$	−26.8922			−1.10807
$590$	−5.19650	−	15.9841i	−0.213937	−	0.658056i
$591$		0			0
$592$	−25.8996	+	13.2183i	−1.06447	+	0.543267i
$593$	−17.5925	+	17.5925i	−0.722439	+	0.722439i	−0.969101	−	0.246663i	$-0.920666\pi$
$593$	−17.5925	+	17.5925i	−0.722439	+	0.722439i	0.246663	+	0.969101i	$0.420666\pi$
$594$		0			0
$595$		−	69.0838i		−	2.83216i
$596$	4.11056	−	26.0091i	0.168375	−	1.06537i
$597$		0			0
$598$	−13.6559	+	6.32371i	−0.558429	+	0.258596i
$599$			12.8652i			0.525659i	0.964842	+	0.262829i	$0.0846556\pi$
$599$			12.8652i			0.525659i	−0.964842	+	0.262829i	$0.915344\pi$
$600$		0			0
$601$	25.5562			1.04246			0.521230	−	0.853416i	$-0.325473\pi$
$601$	25.5562			1.04246			0.521230	+	0.853416i	$0.325473\pi$
$602$	−8.34185	+	16.3785i	−0.339988	+	0.667540i
$603$		0			0
$604$	−17.3495	−	2.74196i	−0.705940	−	0.111569i
$605$	−17.1216	−	17.1216i	−0.696094	−	0.696094i
$606$		0			0
$607$		−	31.7217i		−	1.28754i	−0.765218	−	0.643771i	$-0.777369\pi$
$607$		−	31.7217i		−	1.28754i	0.765218	−	0.643771i	$-0.222631\pi$
$608$	−24.8410	+	24.8824i	−1.00744	+	1.00912i
$609$		0			0
$610$	−3.99230	−	2.03334i	−0.161644	−	0.0823276i
$611$	25.6648	+	20.1685i	1.03828	+	0.815929i
$612$		0			0
$613$	−11.2028	+	11.2028i	−0.452477	+	0.452477i	−0.896176	−	0.443699i	$-0.853666\pi$
$613$	−11.2028	+	11.2028i	−0.452477	+	0.452477i	0.443699	+	0.896176i	$0.353666\pi$
$614$	−10.5661	+	20.7457i	−0.426413	+	0.837227i
$615$		0			0
$616$	−11.0315	+	15.1996i	−0.444473	+	0.612408i
$617$	−13.6394	−	13.6394i	−0.549100	−	0.549100i	0.377080	−	0.926181i	$-0.376928\pi$
$617$	−13.6394	−	13.6394i	−0.549100	−	0.549100i	−0.926181	+	0.377080i	$0.876928\pi$
$618$		0			0
$619$	24.5702	−	24.5702i	0.987561	−	0.987561i	−0.0123622	−	0.999924i	$-0.503935\pi$
$619$	24.5702	−	24.5702i	0.987561	−	0.987561i	0.999924	+	0.0123622i	$0.00393510\pi$
$620$	14.2531	+	19.6040i	0.572418	+	0.787314i
$621$		0			0
$622$	19.1941	−	6.24008i	0.769614	−	0.250204i
$623$	25.9440			1.03942
$624$		0			0
$625$	31.1307			1.24523
$626$	−27.5400	+	8.95336i	−1.10072	+	0.357848i
$627$		0			0
$628$	−15.2950	−	21.0371i	−0.610338	−	0.839470i
$629$	−29.3022	+	29.3022i	−1.16835	+	1.16835i
$630$		0			0
$631$	14.4587	+	14.4587i	0.575593	+	0.575593i	0.933686	−	0.358093i	$-0.116573\pi$
$631$	14.4587	+	14.4587i	0.575593	+	0.575593i	−0.358093	+	0.933686i	$0.616573\pi$
$632$	10.2277	+	7.42303i	0.406835	+	0.295272i
$633$		0			0
$634$	16.7485	−	32.8843i	0.665167	−	1.30600i
$635$	−10.3566	+	10.3566i	−0.410991	+	0.410991i
$636$		0			0
$637$	−5.03146	−	41.9570i	−0.199354	−	1.66240i
$638$	13.4616	+	6.85620i	0.532950	+	0.271440i
$639$		0			0
$640$	31.3048	+	4.92079i	1.23743	+	0.194511i
$641$		−	29.9697i		−	1.18373i	−0.806037	−	0.591866i	$-0.798392\pi$
$641$		−	29.9697i		−	1.18373i	0.806037	−	0.591866i	$-0.201608\pi$
$642$		0			0
$643$	−19.9356	−	19.9356i	−0.786183	−	0.786183i	0.194683	−	0.980866i	$-0.437632\pi$
$643$	−19.9356	−	19.9356i	−0.786183	−	0.786183i	−0.980866	+	0.194683i	$0.937632\pi$
$644$	−25.2260	−	3.98679i	−0.994043	−	0.157101i
$645$		0			0
$646$	−22.7408	+	44.6497i	−0.894725	+	1.75672i
$647$	27.3423			1.07494			0.537469	−	0.843283i	$-0.319380\pi$
$647$	27.3423			1.07494			0.537469	+	0.843283i	$0.319380\pi$
$648$		0			0
$649$			6.51179i			0.255610i
$650$	6.09664	+	13.1655i	0.239130	+	0.516393i
$651$		0			0
$652$	1.83694	−	11.6230i	0.0719401	−	0.455194i
$653$			9.37861i			0.367013i	0.983018	+	0.183507i	$0.0587449\pi$
$653$			9.37861i			0.367013i	−0.983018	+	0.183507i	$0.941255\pi$
$654$		0			0
$655$	34.0857	−	34.0857i	1.33184	−	1.33184i
$656$	14.0054	−	7.14787i	0.546819	−	0.279077i
$657$		0			0
$658$	17.1265	+	52.6801i	0.667661	+	2.05368i
$659$	16.9639			0.660821			0.330411	−	0.943837i	$-0.392813\pi$
$659$	16.9639			0.660821			0.330411	+	0.943837i	$0.392813\pi$
$660$		0			0
$661$	29.9758	+	29.9758i	1.16592	+	1.16592i	0.983156	+	0.182768i	$0.0585056\pi$
$661$	29.9758	+	29.9758i	1.16592	+	1.16592i	0.182768	+	0.983156i	$0.441494\pi$
$662$	−17.8190	−	9.07549i	−0.692555	−	0.352729i
$663$		0			0
$664$	38.6733	−	6.14506i	1.50081	−	0.238475i
$665$	−53.2621	−	53.2621i	−2.06541	−	2.06541i
$666$		0			0
$667$			20.5432i			0.795436i
$668$	26.7333	+	4.22501i	1.03434	+	0.163471i
$669$		0			0
$670$	−39.4172	+	12.8147i	−1.52282	+	0.495075i
$671$	1.22740	+	1.22740i	0.0473831	+	0.0473831i
$672$		0			0
$673$		−	6.87865i		−	0.265152i	−0.991173	−	0.132576i	$-0.957675\pi$
$673$		−	6.87865i		−	0.265152i	0.991173	−	0.132576i	$-0.0423249\pi$
$674$	−6.03197	−	18.5540i	−0.232343	−	0.714672i
$675$		0			0
$676$	16.8181	−	19.8281i	0.646849	−	0.762618i
$677$		−	13.0371i		−	0.501057i	−0.968109	−	0.250528i	$-0.919396\pi$
$677$		−	13.0371i		−	0.501057i	0.968109	−	0.250528i	$-0.0806043\pi$
$678$		0			0
$679$			70.8276i			2.71812i
$680$	44.6017	−	7.08707i	1.71040	−	0.271777i
$681$		0			0
$682$	−2.90329	−	8.93036i	−0.111173	−	0.341961i
$683$	20.9718	−	20.9718i	0.802463	−	0.802463i	−0.181017	−	0.983480i	$-0.557939\pi$
$683$	20.9718	−	20.9718i	0.802463	−	0.802463i	0.983480	+	0.181017i	$0.0579389\pi$
$684$		0			0
$685$		−	8.84200i		−	0.337836i
$686$	13.1079	−	25.7362i	0.500460	−	0.982613i
$687$		0			0
$688$	−11.4300	−	3.70543i	−0.435767	−	0.141268i
$689$	−1.83814	−	15.3282i	−0.0700277	−	0.583956i
$690$		0			0
$691$	−33.4370	−	33.4370i	−1.27200	−	1.27200i	−0.945035	−	0.326969i	$-0.893973\pi$
$691$	−33.4370	−	33.4370i	−1.27200	−	1.27200i	−0.326969	−	0.945035i	$-0.606027\pi$
$692$	17.6377	−	12.8236i	0.670487	−	0.487478i
$693$		0			0
$694$	−3.13755	+	1.02003i	−0.119100	+	0.0387198i
$695$	−31.9558	+	31.9558i	−1.21215	+	1.21215i
$696$		0			0
$697$	15.8454	−	15.8454i	0.600185	−	0.600185i
$698$	−26.5237	−	13.5089i	−1.00394	−	0.511321i
$699$		0			0
$700$	−3.84363	+	24.3202i	−0.145276	+	0.919215i
$701$	15.0565			0.568675			0.284338	−	0.958724i	$-0.408226\pi$
$701$	15.0565			0.568675			0.284338	+	0.958724i	$0.408226\pi$
$702$		0			0
$703$			45.1826i			1.70409i
$704$	−10.9448	−	5.56288i	−0.412498	−	0.209659i
$705$		0			0
$706$	6.70092	+	3.41288i	0.252192	+	0.128446i
$707$	−17.3725	−	17.3725i	−0.653360	−	0.653360i
$708$		0			0
$709$	−14.4736	−	14.4736i	−0.543569	−	0.543569i	0.381004	−	0.924573i	$-0.375578\pi$
$709$	−14.4736	−	14.4736i	−0.543569	−	0.543569i	−0.924573	+	0.381004i	$0.875578\pi$
$710$	5.54719	+	17.0628i	0.208182	+	0.640356i
$711$		0			0
$712$	2.66151	+	16.7499i	0.0997442	+	0.627729i
$713$	9.02943	−	9.02943i	0.338155	−	0.338155i
$714$		0			0
$715$	−1.84537	−	15.3884i	−0.0690129	−	0.575494i
$716$	−7.89167	−	10.8543i	−0.294925	−	0.405646i
$717$		0			0
$718$	31.4488	+	16.0174i	1.17366	+	0.597764i
$719$	−30.9497			−1.15423			−0.577114	−	0.816663i	$-0.695821\pi$
$719$	−30.9497			−1.15423			−0.577114	+	0.816663i	$0.695821\pi$
$720$		0			0
$721$	3.69883	+	3.69883i	0.137752	+	0.137752i
$722$	8.58373	+	26.4030i	0.319453	+	0.982619i
$723$		0			0
$724$	−25.6371	+	18.6395i	−0.952797	+	0.692732i
$725$	19.8055			0.735559
$726$		0			0
$727$	34.8766			1.29350			0.646750	−	0.762702i	$-0.276128\pi$
$727$	34.8766			1.29350			0.646750	+	0.762702i	$0.276128\pi$
$728$	42.4425	−	12.0635i	1.57302	−	0.447104i
$729$		0			0
$730$	13.6389	+	41.9526i	0.504800	+	1.55274i
$731$	−17.1239			−0.633350
$732$		0			0
$733$	−2.70878	+	2.70878i	−0.100051	+	0.100051i	−0.755361	−	0.655309i	$-0.772538\pi$
$733$	−2.70878	+	2.70878i	−0.100051	+	0.100051i	0.655309	+	0.755361i	$0.272538\pi$
$734$	−16.2063	−	49.8497i	−0.598187	−	1.83999i
$735$		0			0
$736$	−0.0139064	−	16.6953i	−0.000512596	−	0.615398i
$737$	16.0582			0.591513
$738$		0			0
$739$	−36.0138	+	36.0138i	−1.32479	+	1.32479i	−0.414938	+	0.909850i	$0.636197\pi$
$739$	−36.0138	+	36.0138i	−1.32479	+	1.32479i	−0.909850	+	0.414938i	$0.863803\pi$
$740$	32.9374	−	23.9472i	1.21080	−	0.880316i
$741$		0			0
$742$	11.8903	−	23.3457i	0.436507	−	0.857046i
$743$	−34.5489	+	34.5489i	−1.26747	+	1.26747i	−0.320086	+	0.947388i	$0.603712\pi$
$743$	−34.5489	+	34.5489i	−1.26747	+	1.26747i	−0.947388	+	0.320086i	$0.896288\pi$
$744$		0			0
$745$			36.8773i			1.35108i
$746$	7.51958	+	23.1298i	0.275311	+	0.846841i
$747$		0			0
$748$	−17.2824	−	2.73136i	−0.631906	−	0.0998683i
$749$	−35.5854	−	35.5854i	−1.30026	−	1.30026i
$750$		0			0
$751$	33.5927			1.22582			0.612908	−	0.790154i	$-0.290000\pi$
$751$	33.5927			1.22582			0.612908	+	0.790154i	$0.290000\pi$
$752$	−32.2543	+	16.4615i	−1.17619	+	0.600288i
$753$		0			0
$754$	−14.9142	−	32.2067i	−0.543142	−	1.17290i
$755$	24.5991			0.895254
$756$		0			0
$757$			43.6629i			1.58695i	0.608600	+	0.793477i	$0.291731\pi$
$757$			43.6629i			1.58695i	−0.608600	+	0.793477i	$0.708269\pi$
$758$	−36.8214	−	18.7537i	−1.33741	−	0.681165i
$759$		0			0
$760$	28.9230	−	39.8509i	1.04915	−	1.44554i
$761$	8.82087	−	8.82087i	0.319756	−	0.319756i	−0.528917	−	0.848673i	$-0.677402\pi$
$761$	8.82087	−	8.82087i	0.319756	−	0.319756i	0.848673	+	0.528917i	$0.177402\pi$
$762$		0			0
$763$	−44.8457			−1.62352
$764$	−20.5484	−	28.2626i	−0.743414	−	1.02250i
$765$		0			0
$766$	12.9656	−	25.4570i	0.468467	−	0.919798i
$767$	9.45286	−	12.0289i	0.341323	−	0.434340i
$768$		0			0
$769$	34.6156	+	34.6156i	1.24827	+	1.24827i	0.956483	+	0.291787i	$0.0942499\pi$
$769$	34.6156	+	34.6156i	1.24827	+	1.24827i	0.291787	+	0.956483i	$0.405750\pi$
$770$	11.9371	−	23.4375i	0.430182	−	0.844627i
$771$		0			0
$772$	5.58496	−	35.3382i	0.201007	−	1.27185i
$773$	−29.1933	+	29.1933i	−1.05001	+	1.05001i	−0.0513298	+	0.998682i	$0.516346\pi$
$773$	−29.1933	+	29.1933i	−1.05001	+	1.05001i	−0.998682	+	0.0513298i	$0.983654\pi$
$774$		0			0
$775$	−8.70520	−	8.70520i	−0.312700	−	0.312700i
$776$	−45.7276	+	7.26597i	−1.64153	+	0.260833i
$777$		0			0
$778$	4.07255	−	1.32400i	0.146008	−	0.0474678i
$779$		−	24.4328i		−	0.875397i
$780$		0			0
$781$		−	6.95124i		−	0.248735i
$782$	−7.35622	−	22.6273i	−0.263058	−	0.809151i
$783$		0			0
$784$	44.5958	+	14.4572i	1.59271	+	0.516329i
$785$	25.7569	+	25.7569i	0.919305	+	0.919305i
$786$		0			0
$787$	7.46253	−	7.46253i	0.266011	−	0.266011i	−0.561480	−	0.827490i	$-0.689768\pi$
$787$	7.46253	−	7.46253i	0.266011	−	0.266011i	0.827490	+	0.561480i	$0.189768\pi$
$788$	−1.87329	+	11.8530i	−0.0667330	+	0.422246i
$789$		0			0
$790$	−15.7709	−	8.03236i	−0.561103	−	0.285778i
$791$	46.6862	+	46.6862i	1.65997	+	1.65997i
$792$		0			0
$793$	−0.485562	−	4.04907i	−0.0172428	−	0.143787i
$794$	9.73209	+	4.95671i	0.345379	+	0.175907i
$795$		0			0
$796$	14.3480	−	10.4317i	0.508551	−	0.369743i
$797$	22.8833			0.810568			0.405284	−	0.914191i	$-0.367173\pi$
$797$	22.8833			0.810568			0.405284	+	0.914191i	$0.367173\pi$
$798$		0			0
$799$	−36.4917	+	36.4917i	−1.29098	+	1.29098i
$800$	−16.0958	+	0.0134070i	−0.569074	+	0.000474010i
$801$		0			0
$802$	12.8772	−	25.2832i	0.454708	−	0.892782i
$803$		−	17.0911i		−	0.603132i
$804$		0			0
$805$	35.7669			1.26062
$806$	−7.60065	+	20.7112i	−0.267721	+	0.729521i
$807$		0			0
$808$	9.43381	−	12.9982i	0.331880	−	0.457274i
$809$	−44.2093			−1.55432			−0.777158	−	0.629306i	$-0.783339\pi$
$809$	−44.2093			−1.55432			−0.777158	+	0.629306i	$0.783339\pi$
$810$		0			0
$811$	−2.94966	−	2.94966i	−0.103576	−	0.103576i	0.653420	−	0.756996i	$-0.273334\pi$
$811$	−2.94966	−	2.94966i	−0.103576	−	0.103576i	−0.756996	+	0.653420i	$0.773334\pi$
$812$	9.40265	−	59.4943i	0.329968	−	2.08784i
$813$		0			0
$814$	−15.0042	+	4.87794i	−0.525898	+	0.170972i
$815$			16.4799i			0.577265i
$816$		0			0
$817$	−13.2021	+	13.2021i	−0.461884	+	0.461884i
$818$	−17.4783	−	8.90199i	−0.611116	−	0.311251i
$819$		0			0
$820$	−17.8111	+	12.9496i	−0.621992	+	0.452220i
$821$	21.8863	−	21.8863i	0.763837	−	0.763837i	−0.213177	−	0.977014i	$-0.568381\pi$
$821$	21.8863	−	21.8863i	0.763837	−	0.763837i	0.977014	+	0.213177i	$0.0683811\pi$
$822$		0			0
$823$	−4.14879			−0.144618			−0.0723088	−	0.997382i	$-0.523037\pi$
$823$	−4.14879			−0.144618			−0.0723088	+	0.997382i	$0.523037\pi$
$824$	−2.00858	+	2.76748i	−0.0699723	+	0.0964099i
$825$		0			0
$826$	24.6909	−	8.02711i	0.859107	−	0.279299i
$827$	10.6504	−	10.6504i	0.370350	−	0.370350i	−0.497255	−	0.867605i	$-0.665659\pi$
$827$	10.6504	−	10.6504i	0.370350	−	0.370350i	0.867605	+	0.497255i	$0.165659\pi$
$828$		0			0
$829$	0.216258			0.00751097			0.00375548	−	0.999993i	$-0.498805\pi$
$829$	0.216258			0.00751097			0.00375548	+	0.999993i	$0.498805\pi$
$830$	−52.1537	+	16.9554i	−1.81028	+	0.588530i
$831$		0			0
$832$	12.1425	+	26.1641i	0.420964	+	0.907077i
$833$	66.8111			2.31487
$834$		0			0
$835$	−37.9041			−1.31173
$836$	−15.4301	+	11.2185i	−0.533663	+	0.388000i
$837$		0			0
$838$	−23.5357	+	7.65156i	−0.813028	+	0.264319i
$839$	25.0859	+	25.0859i	0.866061	+	0.866061i	0.992034	−	0.125972i	$-0.0402050\pi$
$839$	25.0859	+	25.0859i	0.866061	+	0.866061i	−0.125972	+	0.992034i	$0.540205\pi$
$840$		0			0
$841$	−19.4502			−0.670695
$842$	−10.8606	+	21.3239i	−0.374281	+	0.734871i
$843$		0			0
$844$	13.7181	−	9.97374i	0.472195	−	0.343310i
$845$	−18.9298	+	31.1052i	−0.651204	+	1.07005i
$846$		0			0
$847$	26.4480	−	26.4480i	0.908766	−	0.908766i
$848$	16.2922	+	5.28165i	0.559475	+	0.181373i
$849$		0			0
$850$	−21.8148	+	7.09207i	−0.748241	+	0.243256i
$851$	−15.1707	−	15.1707i	−0.520044	−	0.520044i
$852$		0			0
$853$	11.0517	+	11.0517i	0.378403	+	0.378403i	0.870526	−	0.492123i	$-0.163779\pi$
$853$	11.0517	+	11.0517i	0.378403	+	0.378403i	−0.492123	+	0.870526i	$0.663779\pi$
$854$	3.14093	−	6.16696i	0.107480	−	0.211029i
$855$		0			0
$856$	19.3240	−	26.6252i	0.660481	−	0.910030i
$857$			51.1359i			1.74677i	0.487031	+	0.873385i	$0.338080\pi$
$857$			51.1359i			1.74677i	−0.487031	+	0.873385i	$0.661920\pi$
$858$		0			0
$859$	7.91145			0.269935			0.134968	−	0.990850i	$-0.456907\pi$
$859$	7.91145			0.269935			0.134968	+	0.990850i	$0.456907\pi$
$860$	16.6214	+	2.62689i	0.566785	+	0.0895763i
$861$		0			0
$862$	0.217758	−	0.427550i	0.00741686	−	0.0145624i
$863$	12.9345	−	12.9345i	0.440294	−	0.440294i	−0.451817	−	0.892111i	$-0.649224\pi$
$863$	12.9345	−	12.9345i	0.440294	−	0.440294i	0.892111	+	0.451817i	$0.149224\pi$
$864$		0			0
$865$	−21.5950	+	21.5950i	−0.734251	+	0.734251i
$866$	−8.78455	−	27.0208i	−0.298511	−	0.918202i
$867$		0			0
$868$	−30.2825	+	22.0170i	−1.02786	+	0.747304i
$869$	4.84861	+	4.84861i	0.164478	+	0.164478i
$870$		0			0
$871$	−29.6637	−	23.3110i	−1.00511	−	0.789862i
$872$	−4.60057	−	28.9532i	−0.155795	−	0.980478i
$873$		0			0
$874$	−23.1166	−	11.7737i	−0.781932	−	0.398250i
$875$			26.1116i			0.882735i
$876$		0			0
$877$	14.4085	−	14.4085i	0.486539	−	0.486539i	−0.420673	−	0.907212i	$-0.638206\pi$
$877$	14.4085	−	14.4085i	0.486539	−	0.486539i	0.907212	+	0.420673i	$0.138206\pi$
$878$	3.35088	−	1.08939i	0.113087	−	0.0367650i
$879$		0			0
$880$	16.3562	+	5.30241i	0.551368	+	0.178744i
$881$			22.8221i			0.768895i	0.923147	+	0.384448i	$0.125608\pi$
$881$			22.8221i			0.768895i	−0.923147	+	0.384448i	$0.874392\pi$
$882$		0			0
$883$			16.8248i			0.566199i	0.959091	+	0.283099i	$0.0913626\pi$
$883$			16.8248i			0.566199i	−0.959091	+	0.283099i	$0.908637\pi$
$884$	27.9600	+	30.1335i	0.940396	+	1.01350i
$885$		0			0
$886$	−18.1823	+	5.91115i	−0.610848	+	0.198589i
$887$			13.8258i			0.464226i	0.972689	+	0.232113i	$0.0745640\pi$
$887$			13.8258i			0.464226i	−0.972689	+	0.232113i	$0.925436\pi$
$888$		0			0
$889$	−15.9981	−	15.9981i	−0.536557	−	0.536557i
$890$	−7.34359	−	22.5885i	−0.246158	−	0.757167i
$891$		0			0
$892$	7.49751	−	47.4397i	0.251035	−	1.58840i
$893$			56.2685i			1.88295i
$894$		0			0
$895$	13.2896	+	13.2896i	0.444223	+	0.444223i
$896$	−7.60121	+	48.3570i	−0.253939	+	1.61550i
$897$		0			0
$898$	−11.6444	+	22.8629i	−0.388579	+	0.762943i
$899$	21.2955	+	21.2955i	0.710244	+	0.710244i
$900$		0			0
$901$	24.4081			0.813151
$902$	8.11365	−	2.63778i	0.270155	−	0.0878284i
$903$		0			0
$904$	−25.3521	+	34.9308i	−0.843197	+	1.16178i
$905$	31.3891	−	31.3891i	1.04341	−	1.04341i
$906$		0			0
$907$		−	0.155764i		−	0.00517206i	−0.999997	−	0.00258603i	$-0.999177\pi$
$907$		−	0.155764i		−	0.00517206i	0.999997	−	0.00258603i	$-0.000823160\pi$
$908$	−24.1131	−	3.81090i	−0.800220	−	0.126469i
$909$		0			0
$910$	−56.0738	+	25.9665i	−1.85883	+	0.860781i
$911$		−	3.37534i		−	0.111830i	−0.998436	−	0.0559150i	$-0.982192\pi$
$911$		−	3.37534i		−	0.111830i	0.998436	−	0.0559150i	$-0.0178076\pi$
$912$		0			0
$913$	21.2470			0.703172
$914$	39.1399	+	19.9346i	1.29463	+	0.659376i
$915$		0			0
$916$	11.6232	+	1.83696i	0.384040	+	0.0606948i
$917$	52.6526	+	52.6526i	1.73874	+	1.73874i
$918$		0			0
$919$		−	25.7638i		−	0.849869i	−0.905224	−	0.424935i	$-0.860297\pi$
$919$		−	25.7638i		−	0.849869i	0.905224	−	0.424935i	$-0.139703\pi$
$920$	3.66921	+	23.0918i	0.120970	+	0.761314i
$921$		0			0
$922$	−18.7254	+	36.7659i	−0.616689	+	1.21082i
$923$	−10.0908	+	12.8407i	−0.332142	+	0.422657i
$924$		0			0
$925$	−14.6259	+	14.6259i	−0.480898	+	0.480898i
$926$	0.142013	+	0.0723294i	0.00466683	+	0.00237689i
$927$		0			0
$928$	39.3752	−	0.0327976i	1.29255	−	0.00107663i
$929$	28.3002	+	28.3002i	0.928499	+	0.928499i	0.997609	−	0.0691097i	$-0.0220159\pi$
$929$	28.3002	+	28.3002i	0.928499	+	0.928499i	−0.0691097	+	0.997609i	$0.522016\pi$
$930$		0			0
$931$	51.5098	−	51.5098i	1.68817	−	1.68817i
$932$	3.28050	+	4.51206i	0.107456	+	0.147798i
$933$		0			0
$934$	9.61473	+	29.5743i	0.314604	+	0.967702i
$935$	24.5040			0.801367
$936$		0			0
$937$	42.3237			1.38266			0.691328	−	0.722541i	$-0.257026\pi$
$937$	42.3237			1.38266			0.691328	+	0.722541i	$0.257026\pi$
$938$	−19.7950	−	60.8884i	−0.646331	−	1.98808i
$939$		0			0
$940$	41.0188	−	29.8228i	1.33789	−	0.972713i
$941$	21.0672	−	21.0672i	0.686769	−	0.686769i	−0.274747	−	0.961517i	$-0.588594\pi$
$941$	21.0672	−	21.0672i	0.686769	−	0.686769i	0.961517	+	0.274747i	$0.0885941\pi$
$942$		0			0
$943$	8.20366	+	8.20366i	0.267148	+	0.267148i
$944$	7.71541	+	15.1174i	0.251115	+	0.492030i
$945$		0			0
$946$	−5.80947	−	2.95886i	−0.188882	−	0.0962007i
$947$	37.8829	−	37.8829i	1.23103	−	1.23103i	0.267459	−	0.963569i	$-0.413816\pi$
$947$	37.8829	−	37.8829i	1.23103	−	1.23103i	0.963569	−	0.267459i	$-0.0861840\pi$
$948$		0			0
$949$	−24.8104	+	31.5716i	−0.805378	+	1.02486i
$950$	−11.3509	+	22.2866i	−0.368271	+	0.723071i
$951$		0			0
$952$	10.9475	+	68.8969i	0.354811	+	2.23296i
$953$			35.9170i			1.16346i	0.813380	+	0.581732i	$0.197625\pi$
$953$			35.9170i			1.16346i	−0.813380	+	0.581732i	$0.802375\pi$
$954$		0			0
$955$	34.6036	+	34.6036i	1.11975	+	1.11975i
$956$	−1.40039	+	8.86084i	−0.0452919	+	0.286580i
$957$		0			0
$958$	−7.69815	−	3.92079i	−0.248716	−	0.126675i
$959$	13.6584			0.441052
$960$		0			0
$961$			12.2798i			0.396124i
$962$	34.7977	+	12.7701i	1.12192	+	0.411726i
$963$		0			0
$964$	−8.75263	+	55.3814i	−0.281903	+	1.78371i
$965$			50.1047i			1.61293i
$966$		0			0
$967$	−24.7361	+	24.7361i	−0.795460	+	0.795460i	−0.982376	−	0.186916i	$-0.940151\pi$
$967$	−24.7361	+	24.7361i	−0.795460	+	0.795460i	0.186916	+	0.982376i	$0.440151\pi$
$968$	19.7885	+	14.3621i	0.636028	+	0.461616i
$969$		0			0
$970$	61.6669	−	20.0482i	1.98001	−	0.643708i
$971$	19.1899			0.615834			0.307917	−	0.951413i	$-0.400368\pi$
$971$	19.1899			0.615834			0.307917	+	0.951413i	$0.400368\pi$
$972$		0			0
$973$	−49.3625	−	49.3625i	−1.58249	−	1.58249i
$974$	−25.9509	+	50.9525i	−0.831520	+	1.63262i
$975$		0			0
$976$	4.30372	+	1.39519i	0.137759	+	0.0446591i
$977$	22.9975	+	22.9975i	0.735755	+	0.735755i	0.971753	−	0.235999i	$-0.0758361\pi$
$977$	22.9975	+	22.9975i	0.735755	+	0.735755i	−0.235999	+	0.971753i	$0.575836\pi$
$978$		0			0
$979$			9.20234i			0.294108i
$980$	−64.8505	−	10.2492i	−2.07157	−	0.327397i
$981$		0			0
$982$	−5.46060	−	16.7965i	−0.174255	−	0.535997i
$983$	1.02696	+	1.02696i	0.0327549	+	0.0327549i	0.723295	−	0.690540i	$-0.242627\pi$
$983$	1.02696	+	1.02696i	0.0327549	+	0.0327549i	−0.690540	+	0.723295i	$0.742627\pi$
$984$		0			0
$985$		−	16.8059i		−	0.535482i
$986$	53.3654	−	17.3493i	1.69950	−	0.552515i
$987$		0			0
$988$	44.7888	+	1.67575i	1.42492	+	0.0533127i
$989$		−	8.86560i		−	0.281910i
$990$		0			0
$991$		−	57.0449i		−	1.81209i	−0.423181	−	0.906045i	$-0.639087\pi$
$991$		−	57.0449i		−	1.81209i	0.423181	−	0.906045i	$-0.360913\pi$
$992$	−17.3211	−	17.2923i	−0.549946	−	0.549031i
$993$		0			0
$994$	−26.3572	+	8.56882i	−0.835999	+	0.271786i
$995$	−17.5671	+	17.5671i	−0.556914	+	0.556914i
$996$		0			0
$997$		−	12.0315i		−	0.381042i	−0.981683	−	0.190521i	$-0.938982\pi$
$997$		−	12.0315i		−	0.381042i	0.981683	−	0.190521i	$-0.0610177\pi$
$998$	18.3332	+	9.33740i	0.580328	+	0.295570i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.w.j.307.10		24
3.2	odd	2		312.2.t.e.307.3	yes	24
8.3	odd	2	inner	936.2.w.j.307.5		24
12.11	even	2		1248.2.bb.f.463.11		24
13.5	odd	4	inner	936.2.w.j.811.5		24
24.5	odd	2		1248.2.bb.f.463.2		24
24.11	even	2		312.2.t.e.307.8	yes	24
39.5	even	4		312.2.t.e.187.8	yes	24
104.83	even	4	inner	936.2.w.j.811.10		24
156.83	odd	4		1248.2.bb.f.655.2		24
312.5	even	4		1248.2.bb.f.655.11		24
312.83	odd	4		312.2.t.e.187.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.t.e.187.3	✓	24	312.83	odd	4
312.2.t.e.187.8	yes	24	39.5	even	4
312.2.t.e.307.3	yes	24	3.2	odd	2
312.2.t.e.307.8	yes	24	24.11	even	2
936.2.w.j.307.5		24	8.3	odd	2	inner
936.2.w.j.307.10		24	1.1	even	1	trivial
936.2.w.j.811.5		24	13.5	odd	4	inner
936.2.w.j.811.10		24	104.83	even	4	inner
1248.2.bb.f.463.2		24	24.5	odd	2
1248.2.bb.f.463.11		24	12.11	even	2
1248.2.bb.f.655.2		24	156.83	odd	4
1248.2.bb.f.655.11		24	312.5	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34492 - 0.437240i) q^{2} +(1.61764 - 1.17611i) q^{4} +(-1.98058 + 1.98058i) q^{5} +(-3.05943 - 3.05943i) q^{7} +(1.66136 - 2.28908i) q^{8} +(-1.79774 + 3.52971i) q^{10} +(1.08518 - 1.08518i) q^{11} +(-3.57990 + 0.429300i) q^{13} +(-5.45240 - 2.77699i) q^{14} +(1.23353 - 3.80505i) q^{16} -5.70052i q^{17} +(-4.39498 - 4.39498i) q^{19} +(-0.874489 + 5.53324i) q^{20} +(0.984999 - 1.93397i) q^{22} +2.95135 q^{23} -2.84537i q^{25} +(-4.62699 + 2.14265i) q^{26} +(-8.54727 - 1.35084i) q^{28} +6.96062i q^{29} +(3.05943 - 3.05943i) q^{31} +(-0.00471188 - 5.65685i) q^{32} +(-2.49250 - 7.66677i) q^{34} +12.1189 q^{35} +(-5.14026 - 5.14026i) q^{37} +(-7.83257 - 3.98925i) q^{38} +(1.24323 + 7.82415i) q^{40} +(2.77963 + 2.77963i) q^{41} -3.00392i q^{43} +(0.479142 - 3.03172i) q^{44} +(3.96934 - 1.29045i) q^{46} +(-6.40146 - 6.40146i) q^{47} +11.7202i q^{49} +(-1.24411 - 3.82681i) q^{50} +(-5.28610 + 4.90481i) q^{52} +4.28172i q^{53} +4.29856i q^{55} +(-12.0861 + 1.92044i) q^{56} +(3.04346 + 9.36150i) q^{58} +(-3.00033 + 3.00033i) q^{59} +1.13106i q^{61} +(2.77699 - 5.45240i) q^{62} +(-2.47974 - 7.60598i) q^{64} +(6.24001 - 7.94053i) q^{65} +(7.39889 + 7.39889i) q^{67} +(-6.70444 - 9.22140i) q^{68} +(16.2989 - 5.29885i) q^{70} +(3.20281 - 3.20281i) q^{71} +(7.87480 - 7.87480i) q^{73} +(-9.16078 - 4.66573i) q^{74} +(-12.2785 - 1.94053i) q^{76} -6.64004 q^{77} +4.46803i q^{79} +(5.09309 + 9.97930i) q^{80} +(4.95376 + 2.52303i) q^{82} +(9.78962 + 9.78962i) q^{83} +(11.2903 + 11.2903i) q^{85} +(-1.31343 - 4.04004i) q^{86} +(-0.681180 - 4.28693i) q^{88} +(-4.24001 + 4.24001i) q^{89} +(12.2659 + 9.63903i) q^{91} +(4.77422 - 3.47111i) q^{92} +(-11.4085 - 5.81050i) q^{94} +17.4092 q^{95} +(-11.5753 - 11.5753i) q^{97} +(5.12453 + 15.7627i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{8} - 8 q^{11} - 36 q^{14} + 28 q^{16} + 20 q^{19} + 20 q^{20} + 20 q^{22} - 12 q^{26} - 16 q^{28} + 30 q^{32} + 16 q^{34} - 16 q^{35} + 36 q^{40} + 12 q^{41} + 32 q^{44} - 44 q^{46} + 36 q^{50}+ \cdots - 68 q^{98}+O(q^{100}) \) 24 * q + 6 * q^8 - 8 * q^11 - 36 * q^14 + 28 * q^16 + 20 * q^19 + 20 * q^20 + 20 * q^22 - 12 * q^26 - 16 * q^28 + 30 * q^32 + 16 * q^34 - 16 * q^35 + 36 * q^40 + 12 * q^41 + 32 * q^44 - 44 * q^46 + 36 * q^50 + 4 * q^52 + 32 * q^58 + 16 * q^59 + 76 * q^65 + 28 * q^67 - 32 * q^68 - 40 * q^70 - 8 * q^73 + 32 * q^74 - 36 * q^76 + 32 * q^80 + 72 * q^83 - 4 * q^86 - 28 * q^89 - 4 * q^91 - 32 * q^92 + 28 * q^94 + 24 * q^97 - 68 * q^98

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